The purpose of this research is to develop original understanding of chemometric techniques in order to optimize concentration predictions from spectral data. We have developed an original formula to express partial least squares (PLS) and principal component regression (PCR) calibrations in a simple linear form and have derived an analytical expression for spectral error propagation through these algorithms in the limit of zero calibration error. We plan to extend this investigation to consider the propagation of errors in reference concentrations and in calibration spectra.